Classifications

• • H—ELECTRICITY
  • H01—ELECTRIC ELEMENTS
  • H01J—ELECTRIC DISCHARGE TUBES OR DISCHARGE LAMPS
  • H01J37/00—Discharge tubes with provision for introducing objects or material to be exposed to the discharge, e.g. for the purpose of examination or processing thereof
  • H01J37/32—Gas-filled discharge tubes
  • H01J37/32009—Arrangements for generation of plasma specially adapted for examination or treatment of objects, e.g. plasma sources
  • H01J37/32082—Radio frequency generated discharge
• • H—ELECTRICITY
  • H03—ELECTRONIC CIRCUITRY
  • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
  • H03H11/00—Networks using active elements
  • H03H11/02—Multiple-port networks
  • H03H11/04—Frequency selective two-port networks
  • H03H11/12—Frequency selective two-port networks using amplifiers with feedback
  • H03H11/1291—Current or voltage controlled filters
• • H—ELECTRICITY
  • H03—ELECTRONIC CIRCUITRY
  • H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
  • H03H7/00—Multiple-port networks comprising only passive electrical elements as network components
  • H03H7/38—Impedance-matching networks
  • H03H7/40—Automatic matching of load impedance to source impedance
• • H—ELECTRICITY
  • H05—ELECTRIC TECHNIQUES NOT OTHERWISE PROVIDED FOR
  • H05H—PLASMA TECHNIQUE; PRODUCTION OF ACCELERATED ELECTRICALLY-CHARGED PARTICLES OR OF NEUTRONS; PRODUCTION OR ACCELERATION OF NEUTRAL MOLECULAR OR ATOMIC BEAMS
  • H05H1/00—Generating plasma; Handling plasma
  • H05H1/24—Generating plasma
  • H05H1/46—Generating plasma using applied electromagnetic fields, e.g. high frequency or microwave energy
• • H—ELECTRICITY
  • H05—ELECTRIC TECHNIQUES NOT OTHERWISE PROVIDED FOR
  • H05H—PLASMA TECHNIQUE; PRODUCTION OF ACCELERATED ELECTRICALLY-CHARGED PARTICLES OR OF NEUTRONS; PRODUCTION OR ACCELERATION OF NEUTRAL MOLECULAR OR ATOMIC BEAMS
  • H05H2242/00—Auxiliary systems
  • H05H2242/20—Power circuits
  • H05H2242/26—Matching networks

Definitions

• the present invention relates generally to electrical generators.
• the present invention relates to methods and apparatuses for tuning (adjusting) the operational frequency of a generator.
• Power generators are typically designed for optimal performance into a specific load impedance, typically 50 ohms. Operating into a load impedance close to the design value typically results in the highest output power capability and the lowest stress on the components internal to the generator. Typically, but not always, some type of matching network is used to match the load to the generator. By correct design of the matching network (either internal to the generator or external), it is possible to transform the impedance of the load to a value close to the desired load impedance at some frequency in the range of frequencies that the generator can produce.
• Many embodiments of the present invention provide a method and apparatus for rapidly tuning the operational frequency of a generator (e.g., an RF generator) in response to changes in load impedance of a nonlinear and/or time-varying load coupled to the generator.
• a generator e.g., an RF generator
• One illustrative embodiment comprises a method of frequency tuning, the method including calculating the load reflection coefficient and then adjusting the generator's operating frequency based on the relative magnitude of the calculated load reflection coefficient as compared with one or more previously calculated load reflection coefficients.
• Another illustrative embodiment comprises a method of frequency tuning, the method including calculating the load reflection coefficient and then adjusting a frequency step size based on the relative magnitude of the calculated load reflection coefficient as compared with one or more previously calculated load reflection coefficients.
• Yet another illustrative embodiment comprises a method of calculating the load reflection coefficient (or other metric) in a rapid time frame relative to the variability of a time-variant load coupled to a generator.
• FIG. 1 is a system-level block diagram depicting a system in which embodiments of the present invention may be realized
• FIG. 2 is a graphical illustration (Smith chart) of the general behavior of the load reflection coefficient as a function of frequency for the system depicted in FIG. 1;
• FIG. 3 is a graphical illustration of an error (here simply the reflection coefficient magnitude) as a function of frequency corresponding to FIG. 2;
• FIG. 4 is a block diagram depicting functional components that may be implemented in connection with the system depicted in FIG. 1 ;
• FIG. 5 is a graphical illustration of the error and frequency as a function of time in the case where an error is a monotonic function of frequency
• FIG. 6 is a graphical illustration of an error and frequency as a function of time for the case where methods in accordance with embodiments of the present invention are beneficial;
• FIG. 7 is a graphical illustration of an error function as a function of frequency for a time-invariant (linear or nonlinear) load
• FIG. 8 is a graphical illustration of another error function as a function of frequency for a time-varying (linear or nonlinear) load
• FIG. 9 is a flowchart of a method for finding a desirable frequency in accordance with yet another illustrative embodiment of the disclosed frequency tuning method
• FIG. 10 is a flowchart of a method for finding a desirable frequency in accordance with yet another illustrative embodiment of the disclosed frequency tuning method
• Figs. 11 and 12 are graphs depicting a simulation of exemplary methods carried out in connection with embodiments exposed to noise;
• Figs. 13 and 14 are graphs depicting a simulation of exemplary methods carried out in connection with embodiments in the absence of noise;
• Figs. 15 and 16 are graphs depicting a simulation of additional exemplary methods carried out in connection with embodiments in the absence of noise;
• Figs. 17 and 18 are graphs that illustrate a failure of a stabilized method to tune in the presence of noise
• Figures 19, 20 and 21 are graphs that graphically illustrate inter-pulse frequency tuning in accordance with one or more embodiments of the disclosed frequency tuning method
• FIG. 22 graphically illustrates an exemplary frequency tuning method which uses a small percentage of time with a maximum time slot of duration T to search for a global optimum frequency.
• Frequency tuning in generators is often used to reduce reflected power and thereby obtain efficient operation.
• FIG. 1 a block diagram of a typical generation system 100 is shown.
• a generator 102 is electrically coupled to a load 106.
• some type of matching network 104 is used to match the load to the generator.
• the measure of how close the load impedance is to the desired impedance can take many forms, but typically it is expressed as a reflection coefficient
• a desirable frequency of operation is a frequency at which the magnitude of the load reflection coefficient is at or substantially close to its minimum
• the relationship between the controlled variable (frequency) and the error is not necessarily monotonic.
• the optimum point of operation is at a point where the gain (defined as change in error divided by change in frequency) is zero.
• local minima may exist in an area which a control method can get trapped.
• FIG. 2 shows a plot of a load reflection coefficient on a load reflection coefficient chart (Smith chart)
• FIG. 3 shows the corresponding magnitude of the load reflection coefficient used as the error, as a function of frequency.
• FIG. 5 it is a graph depicting an error and frequency that are both monotonic. Such linear control is rarely applicable due to the non-monotonic relationship between frequency and error, except in those special cases where a priori information about the load is available.
• an error e.g., the magnitude of the load reflection coefficient, as a function of frequency
• a frequency tuning algorithm operating at frequency ⁇ and time t 0 and subsequently at frequency f ⁇ at time t ⁇ will correctly determine that Z 1 is a better frequency at which to operate, and will continue to tune to higher frequencies until the minimum error at ⁇ pt i ma i is reached.
• an error e.g., the magnitude of the load reflection coefficient, as a function of frequency
• a typical frequency tuning algorithm operating at frequency _/0 and time to and subsequently at frequency f ⁇ at time t ⁇ will incorrectly determine that/i is a worse frequency at which to operate and will tune away from the optimal frequency. This incorrect result is because the error function itself has changed over time.
• FIG. 4 it is a block diagram depicting functional components of exemplary embodiments, which may be implemented in connection with the embodiment depicted in FIG. I . It should be recognized that the illustrated arrangement of these components is logical and not meant to be an actual hardware diagram. Thus, the components can be combined or further separated in an actual implementation. Moreover, the construction of each individual component, which may include hardware, firmware, software, and combinations thereof, is well-known to those of skill in the art— in light if this specification.
• controller depicted in FIG. 4 are configured to accommodate (e.g., by carrying out control methodologies described further herein) circumstances in which a non-monotonic relationship between an error and the frequency exist (e.g., when a priori information about the load is not known).
• error function depicted in FIG. 4 in many variations indicates non-desirable operation, and in many embodiments indicates non-optimal operation.
• the solution is two-fold.
• the first is the development of a very fast division methodology that allows the calculation of the load reflection coefficient at speeds significantly faster (up to one thousand times faster) than what is traditionally used.
• the second part of the solution in these embodiments is to allow the frequency step size to increase if the error is decreasing step-over-step, and decrease (or stay constant) if the error is increasing step-over-step.
• the problem of keeping up with a time-varying load is solved. It is certainly contemplated, however, that alternatives to the specific fast division methodology disclosed herein may be utilized (if sufficiently fast) in connection with the above-identified second part of the solution.
• FIG. 9 depicts a flow diagram 900 illustrating one embodiment of a frequency tuning method in accordance with the present invention, which may be carried out, at least in part, by the controller depicted in FIG. 4.
• the method initiates at block 902, typically, but not always, at power up.
• the method rapidly calculates the load reflection coefficient (e.g., using a very fast division method that allows the calculation of the load reflection coefficient at speeds significantly faster (e.g., up to one thousand times faster) than what is traditionally used). Calculation in this context may be in the order of microseconds (depending on the specific implementation), which is rapid relative to the rate at which the load varies in time, typically in the order of milliseconds.
• a specific method for arriving at the load reflection coefficient is described in detail herein, other methodologies for calculating the load reflection coefficient are certainly contemplated.
• the method determines whether the error is decreasing relative to the previous error (or errors) calculated.
• the frequency step size by which the frequency is adjusted
• the method branches to block 910, where the frequency step size is decreased or (left at the present value).
• the method progresses to block 912, where the new frequency is set (based on the applicable step size) and the method cycles through again.
• the rapid division method disclosed herein makes use of the fact that the reflection coefficient is a complex number with magnitude between 0 and 1. Treating the real and imaginary parts of the reflection coefficient separately, and determining the sign of the result from the signs of the numerator and denominator, or when only calculating the magnitude of the reflection coefficient (or, more typically the square of the magnitude of the reflection coefficient by dividing reflected power by forward power), the problem is reduced to the calculation of the ratio of two positive real numbers. When it is known that the answer must be between 0 and 1, it allows for an iterative solution without ever having to perform multiplication operations. Note that in the specific application, it can be assumed that the denominator is never zero because the denominator is generally proportional to the square root of forward power, which is never zero during operation, when this calculation is required.
• the calculation is performed in fixed point n arithmetic, and therefore we assign a power of 2, for example 2 , to represent a ratio of one. With this assignment, we have
• 2 n x N RxD where N, R and D are integers.
• the calculation of 2 n x N can be performed inexpensively (in terms of computing resources) as a left-shift operation on the binary representation of N. [0032] The calculation starts by calculating low, middle and upper estimates of what R is. n
• the initial low estimate is simply 0, the initial upper estimate, 2 , represents a ratio of 1 and the initial middle estimate is 2 (n"1) .
• R x D arc calculated as 0, 2 ( " "! x D and 2 n x D, respectively. Note that the middle and upper estimates for the product can again be calculated efficiently as left shifts of the binary representations of D by n-1 and n, respectively.
• the calculation iterates by comparing the middle estimate of the product to the required value, T x N. If the middle estimate is greater than 2 n x N, then the middle estimate becomes the new upper estimate; otherwise the middle estimate becomes the new low estimate. A new middle estimate is calculated as half the sum of the new low and upper estimates. This calculation is performed as a sum followed by a right shift, again using computationally non-intensive numerical processing techniques. By maintaining extra fractional bits, rounding errors can be avoided.
• the reflection coefficient (or its magnitude) is available for use by the frequency tuning method with sufficient accuracy and within a fraction of a microsecond after the new values for the forward and reflected signals are available, allowing for very fast tuning. For example, when using 8-bit estimates of the ratio, and a 64 MHz clock, the ratio is calculated in 125 nanoseconds. Typically the noisy nature of the plasma load limits the maximum frequency update rate to a few microseconds, so this method efficiently provides the required calculation in adequate time to deliver a fast and effective frequency tuning capability.
• FIG. 10 depicts a flow diagram 1000 illustrating another variation of the disclosed frequency tuning methodology.
• the method starts at initial power up of the generator system 100, or if frequency tuning is enabled.
• the method sets the frequency to ⁇ t an and the frequency step to/ step ⁇ .
• the method waits until RF is turned on.
• the error at the new frequency is measured at block 1018.
• the error, e > is compared to the previous error, eo.
• the frequency step magnitude is changed to the maximum frequency step, ⁇ t ep •
• the frequency is changed by the frequency step, ./ step , and limited to the range between the minimum frequency and the maximum frequency [0042] If the error, e, is greater than the previous error, eo, as determined in block 1020 then the method progresses to block 1026 where the frequency is changed by minus one- half the current step size, i.e., one-half of the last step is undone.
• the frequency step, f iXep is multiplied by negative g ⁇
• the frequency step magnitude is changed to the minimum frequency step size, /step . .
• the previous error gets assigned the value of the current error, e.
• the case where RF is turned off while tuning is in progress is handled.
• the error is compared to a lower threshold. If the error is less than the threshold, the method enters the loop created by blocks 1042, 1044, 1046 and 1052 and will remain in this state until the error exceeds an upper threshold as detected in block 1042 or RF is turned off as detected in block 1046. If, on the other hand, the error is larger than the lower threshold as determined in block 1038, the method proceeds to block 1040 where a determination is made as to whether or not a tune time is exceeded.
• the generator is allowed to operate at the new frequency until a new measurement of the error e is obtained as shown in block 1018.
• the time that is spent at the new frequency is a function of the load and measurement system characteristics, but is generally on the order of 10 microseconds.
• a determination of whether the error is less than an upper threshold is made in block 1042. If the error is less than the upper threshold the method enters the loop created by blocks 1042, 1044, 1046 and 1052 and will remain in this state until the error exceeds an upper threshold as detected in block 1042 or RF is turned off as detected in block 1046. If the tune time has been exceeded and the error is larger than the upper threshold as determined in block 1042, a failure to tune timer is started and the method is allowed to continue trying to tune to the upper threshold until this failure to tune time is exceeded as determined in block 1054. If the method failed to tune, an error is declared and RF may be turned off depending on the user settings.
• the exemplary method depicted in FIG. 10 is augmented by conditions for starting and stopping the tuning method. For example, as illustrated at branches 1038 and 1042, a lower and upper target for the error, as well as a time to get to the lower target, are typically set. The tuning method will then attempt to get to the lower target in the allotted time. If it reaches the lower target the method stops, as illustrated at block 1038, If the allotted time is exceeded, the method stops if the error is less than the upper target, as illustrated at block 1042. Once the method is stopped, it is generally re-started when the upper target is exceeded. If the method fails to reach the upper or lower targets, errors and warnings may be issued to the system controller.
• the method can be further augmented by doing an initial frequency sweep when power (e.g., RF power) is first turned on to find the optimal operating point with some degree of accuracy before starting the frequency tuning method.
• the sweep is generally carried out in both directions because the effects of ignition, or failure to ignite, may mask the true minimum.
• the plasma may ignite at one frequency, but once ignited, the plasma may operate at a different, higher optimum frequency. If the frequency is swept from low to high, the optimum frequency will be found, but not if it is swept from high to low, since the plasma will not be ignited when the higher, optimal frequency is probed.
• Further enhancements include searching for the desirable ignition frequency separately from searching for a desirable operating frequency.
• the desirable ignition frequency corresponds to the frequency at which the load reflection coefficient is minimized with the plasma not ignited.
• a sweep at very low power where the plasma cannot ignite can determine the best ignition frequency under such conditions, which often occur.
• Such waypoints may include a start frequency for ignition, a time to stay at the ignition frequency, then a second frequency with a time to stay at that frequency (and even more frequency, duration points) before starting the regular frequency tuning method.
• ignition may also be detected by looking for a sudden change in load reflection coefficient, delivered, forward or reflected power, or combinations thereof.
• a step down gain, g d may be generally less than 0.5 for stability reasons, with 0.125 being an exemplary value.
• the step up gain, g u is generally set to 2 or 4.
• the minimum frequency is generally set large enough so that when comparing two frequencies, the error is significantly different, and noise does not influence the decision process in the method too much. Correctly setting the smallest frequency step helps to optimize the method.
• the maximum frequency step is generally set such that the method does not jump over minima or extinguish (in the case of plasma loads) the plasma.
• the variables are generally preset, but the user may have the ability to change the settings to optimize the method in specific applications.
• One solution for simultaneous pulsing and frequency tuning discards information at the start of the pulse while the impedance is still rapidly changing and effectively controls by using only information once the load impedance is stable. This approach avoids the need for tuning within the pulse, but manages to obtain a good average frequency of operation.
• the measurement and control may be synchronized with the rising edge of the pulse. By delaying the start of the measurement and control cycle from the start of the pulse, reasonable operation on plasma-type loads is possible. Typically discarding the first 10 microseconds after the start of the pulse is sufficient to achieve reasonable results.
• Figs. 11 and 12 viewed together, illustrate a simulation of the disclosed frequency tuning methodology in the presence of noise.
• the ideal frequency (where the error is at its minimum) is 13 MHz for the first 24 milliseconds, after which the ideal frequency changes to 14MHz.
• the time spent at each frequency in the simulation is 16 microseconds.
• Figs. 13 and 14 viewed together, illustrate a simulation of the disclosed frequency tuning methodology in the absence of noise showing the unstable limit cycle behavior.
• the ideal frequency (where the error is at its minimum) is 13 MHz for the first 24 milliseconds, after which the ideal frequency changes to 14 MHz.
• the time spent at each frequency in the simulation is 16 microseconds.
• Figs. 15 and 16 viewed together, illustrate a simulation of one variation of the disclosed frequency tuning methodology in the absence of noise, with an additional constraint that, after changing direction, the step size is only allowed to increase after [1/(2 x gd)] steps, which enhances stability.
• the ideal frequency (where the error is at its minimum) is 13 MHz for the first 24 milliseconds, after which the ideal frequency changes to 14 MHz.
• the time spent at each frequency in the simulation is 16 microseconds.
• the ideal frequency (where the error is at its minimum) is 13 MHz for the first 24 milliseconds, after which the ideal frequency changes to 14 MHz.
• the time spent at each frequency in the simulation is 16 microseconds.
• control parameters are stored and used by the control system to, for example, control delivered power to the load.
• control parameters may include DC voltage supplied to the power devices, gate bias voltage in the case of MOSFETs (base emitter in case of bipolar devices) and RF drive level.
• FIGs. 19, 20 and 21 Graphs depicting operation of an inter-pulse controled system for a high pulse repetition frequency are shown in FIGs. 19, 20 and 21. If the pulse on time becomes very long, it may be more advantageous to simply ignore information from the first few time slots, or switch to intra-pulse control at some time later in the pulse.
• ⁇ is a function of only (or predominantly if adjacent time slots are also considered with some weighting) e a o, e a i andfai.
• ⁇ ,2 is a function of only (or predominantly) ⁇ b o, and so forth.
• the last problem for which a solution is described is the problem of getting trapped in local non-optimal minima.
• T 5 the method works by operating, for example, 99% of the time at the optimum frequency (as determined by the frequency tuning method) and using the remaining 1% of the time in time slots not exceeding T in duration to explore operation at other frequencies.
• the following method is exemplary and illustrative.
• the entire frequency range from fmia to/nax can be divided into, for example, 16 equally spaced frequencies fo through / 15 .
• the number of frequencies in which to divide the entire frequency range is a function of the known quality factor of the matching circuits employed. Sixteen is a typical number to make sure the true optimal point will not be missed in subsequent searches for the optimal frequency.
• the method may start by sequentially searching ⁇ through / 15 in the time slots of duration T to find a coarse optimum.
• the space may need to be searched a few times because the power control system may not be able to adjust the power correctly within the time T. Due to the nonlinear nature of the typical loads encountered, it is beneficial to measure the load reflection coefficient (or other error metric used by the method) at or close to a desired power level. By storing the control value and power level every time that a frequency is visited, the correct power level can be attained after a few visits to the same frequency.
• the method may start using the time slots of length T to find an optimum.
• the frequency at which the error is at a minimum between/i6, ⁇ and/17 then becomes the new desired frequency.
• the interval to the left and right of the new optimum is again split in two, and the minimum among the previous minimum and the two newly tested frequencies is selected. And when the minimum frequency happens to be/nin or/ max , only one new frequency is generated.
• the optimum frequency is found with sufficient accuracy within just a few iterations. And because the load is generally time-variant, once the optimum frequency has been found, the method generally has to start over to make sure conditions have not changed and a new global optimum has not been created.
• FIG. 22 graphically illustrates exemplary operating characteristics that may be associated with a method which uses a small percentage of the time with a maximum time slot T to search for a global optimum frequency.

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• Physics & Mathematics (AREA)
• Engineering & Computer Science (AREA)
• Plasma & Fusion (AREA)
• Chemical & Material Sciences (AREA)
• Analytical Chemistry (AREA)
• Electromagnetism (AREA)
• Spectroscopy & Molecular Physics (AREA)
• Plasma Technology (AREA)
• Channel Selection Circuits, Automatic Tuning Circuits (AREA)

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• 2008
  • 2008-09-30 US US12/242,328 patent/US7839223B2/en active Active
• 2009
  • 2009-03-12 WO PCT/US2009/037001 patent/WO2009120514A2/en active Application Filing
  • 2009-03-12 CN CN2009801188392A patent/CN102037789A/zh active Pending
  • 2009-03-12 KR KR1020107021902A patent/KR101175644B1/ko not_active IP Right Cessation
  • 2009-03-12 EP EP09724338.0A patent/EP2258150A4/en not_active Withdrawn
  • 2009-03-12 JP JP2011501896A patent/JP2011515823A/ja not_active Withdrawn
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